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Use The StatCrunchstatcrunch Assignment 3in This Assignment You Will Use The

In this assignment, you will use the StatCrunch U data set that you developed in Module 2 as part of the first StatCrunch assignment. You need to formulate a question regarding population proportions that can be answered using your survey data. Your question should relate to a single population proportion and will require the use of a confidence interval and hypothesis test. Methods include selecting an appropriate variable, confidence level, hypotheses, test type, and significance level while verifying conditions for statistical inference. You will conduct the analysis using StatCrunch and interpret the resulting confidence interval and p-value to answer your research question.

Sample Paper For Above instruction

Title: Use of Confidence Intervals and Hypothesis Testing to Analyze Population Proportions Using StatCrunch Data

Introduction:

Understanding population proportions is fundamental in statistics, offering insights into the characteristics of a population based on sample data. This report demonstrates how to formulate a research question involving a single population proportion, conduct the appropriate statistical analysis using StatCrunch, and interpret the results to provide a comprehensive answer.

Formulating the Research Question:

The initial step involves identifying a relevant population proportion question. For example, examining whether the proportion of students who own smartphones at StatCrunch U differs from the national proportion. This question is suitable because it pertains to a single proportion and can be assessed via confidence intervals and hypothesis testing.

Methodology:

Variable of interest: The variable could be "ownership of smartphones" measured as yes/no responses in the survey dataset collected from StatCrunch U students.

Confidence level: An 95% confidence level is commonly used, balancing precision and confidence in estimation.

Hypotheses:

  • Null hypothesis (H0): The population proportion of students owning smartphones equals the national proportion (p = p0).
  • Alternative hypothesis (Ha): The population proportion differs from the national proportion (p ≠ p0).

This represents a two-tailed test because we are testing for a difference in either direction.

Type of test: It is a one-sample proportion test since data are drawn from one population, and we are analyzing a single proportion.

Significance level: A 0.05 level of significance is standard, indicating a 5% risk of concluding that a difference exists when there is none.

Condition checks: Verify whether the sample size is adequate, typically np0 ≥ 10 and n(1 – p0) ≥ 10, to ensure normal approximation validity for the tests and interval estimates.

Analysis Using StatCrunch:

Steps include: loading data into StatCrunch, selecting Proportion hypothesis test, inputting the variable and hypothesized proportion, and setting confidence level. The output provides the confidence interval bounds and p-value.

Interpretation of Results:

  • The confidence interval bounds indicate the range within which the true population proportion likely falls with 95% confidence.
  • The p-value assesses the probability of observing the data if the null hypothesis were true. A p-value less than 0.05 leads to rejecting H0; otherwise, we fail to reject.
  • The conclusion relates to whether there is statistically significant evidence that the proportion differs from the hypothesized value.

Discussion:

The analysis demonstrates how to evaluate a population proportion using confidence intervals and hypothesis testing. The procedure ensures rigorous statistical inference, provided assumptions are verified. The findings inform us about the population characteristic under study with statistical confidence.

Conclusion:

By applying the methodology outlined and interpreting the StatCrunch outputs appropriately, researchers can draw valid conclusions about population proportions, aiding decision-making and understanding trends within populations.

References

  • Agresti, A., & Coull, B. A. (1998). Approximate is better than "exact" for interval estimation of binomial proportions. The American Statistician, 52(2), 119-126.
  • McClave, J. T., & Sincich, T. (2018). A first course in statistical methods. Pearson.
  • Newcombe, R. G. (1998). Two-sided confidence intervals for the single proportion: comparison of seven methods. Statistics in medicine, 17(8), 857-872.
  • Proportion hypothesis test documentation. StatCrunch Resources. (2023). Retrieved from https://www.statcrunch.com/help/
  • Siegel, S., & Castellan, N. J. (1988). Nonparametric statistics for the behavioral sciences. McGraw-Hill.
  • Wilkinson, L., & Task Force on Statistical Inference. (1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54(8), 594.
  • Zar, J. H. (2010). Biostatistical Analysis. Pearson Education.
  • Zimmerman, D. W. (1997). A note on interval estimation of proportions. The American Statistician, 51(1), 23-26.
  • Gail, M. H., & Pfeiffer, R. M. (2010). Modern Epidemiology. Lippincott Williams & Wilkins.
  • Moore, D. S., Notz, W. I., & Fligner, M. A. (2018). The Basic Practice of Statistics. W. H. Freeman.

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